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Simultaneous prediction intervals for ARMA processes with stable innovations
Author(s) -
Nolan John P.,
Ravishanker Nalini
Publication year - 2009
Publication title -
journal of forecasting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.543
H-Index - 59
eISSN - 1099-131X
pISSN - 0277-6693
DOI - 10.1002/for.1102
Subject(s) - monte carlo method , autoregressive–moving average model , interval (graph theory) , series (stratigraphy) , computation , stability (learning theory) , measure (data warehouse) , mathematics , prediction interval , computer science , econometrics , statistics , algorithm , autoregressive model , statistical physics , data mining , machine learning , physics , paleontology , combinatorics , biology
We describe a method for calculating simultaneous prediction intervals for ARMA times series with heavy‐tailed stable innovations. The spectral measure of the vector of prediction errors is shown to be discrete. Direct computation of high‐dimensional stable probabilities is not feasible, but we show that Monte Carlo estimates of the interval width is practical. Copyright © 2008 John Wiley & Sons, Ltd.